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If y^1/m + y^-1/m = 2x

show that (x^2-1)y2+xy1-m^2y=0

$y^{\frac{1}{m}} + y^{- \frac{1}{m}} = 2 x y^{\frac{1}{m}} - y^{- \frac{1}{m}} = 2 \sqrt{x^{2} - 1} (\frac{1}{m} y^{\frac{1}{m} - 1} - \frac{1}{m} y^{- \frac{1}{m} - 1}) y_{1} = 2 (y^{\frac{1}{m}} - y^{- \frac{1}{m}}) y_{1} = 2 m y (y^{\frac{1}{m}} - y^{- \frac{1}{m}}) y_{2} + \frac{1}{m} (y^{\frac{1}{m} - 1} + y^{- \frac{1}{m} - 1}) y_{1}^{2} = 2 m y_{1} (y^{\frac{1}{m}} - y^{- \frac{1}{m}}) y_{2} + \frac{2 x y_{1}}{m y} \times \frac{2 m y}{2 \sqrt{(x^{2} - 1)}} = 2 m y_{1} 2 \sqrt{x^{2} - 1} y_{2} + \frac{4 x y_{1}}{2 \sqrt{x^{2} - 1}} = 2 m y_{1} (x^{2} - 1) y_{2} + x y_{1} = m y_{1} \sqrt{x^{2} - 1} = m^{2} y (x^{2} - 1) y_{2} + x y_{1} - m^{2} y = 0$

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